General Relativity and Quantum Cosmology

Title:
Uniqueness of the Kerr-de Sitter spacetime as an algebraically special solution in five dimensions

Abstract: We determine the most general solution of the five-dimensional vacuum
Einstein equation, allowing for a cosmological constant, with (i) a Weyl tensor
that is type II or more special in the classification of Coley et al., (ii) a
non-degenerate "optical matrix" encoding the expansion, rotation and shear of
the aligned null direction. The solution is specified by three parameters. It
is locally isometric to the 5d Kerr-de Sitter solution, or related to this
solution by analytic continuation or taking a limit. This is in contrast with
four dimensions, where there exist infinitely many solutions with properties
(i) and (ii).